Points and lines connected with a triangle : The extended law of sines ; Ceva’s theorem ; Points of interest ; The incircle and excircles ; The Steiner-Lehmus theorem ; The orthic triangle ; The medial triangle and Euler line ; The nine-point circle ; Pedal triangles --
Some properties of circles : The power of a point with respect to circles ; The radical axis of two circles ; Coaxal circles ; More on the altitudes and orthocenter of a triangle ; Simson lines ; Ptolemy’s theorem and its extension ; More on Simson lines ; The butterfly ; Morley’s theorem --
Collinearity and concurrence : Quadrangles; Varignon’s theorem ; Cyclic quadrangles; Brahmagupta’s formula ; Napoleon triangles ; Menelaus’s theorem ; Pappus’s theorem ; Perspective triangles; Desargues’s theorem ; Hexagons ; Pascal’s theorem ; Brianchon’s theorem --
Transformations : Translation ; Rotation ; Half-turn ; Reflection ; Fagnano’s problem ; The three jug problem ; Dilatation ; Spiral similarity ; A genealogy of transformations --
An introduction to inversive geometry : Separation ; Cross ratio ; Inversion ; The inversive plane ; Orthogonality ; Feuerbach’s theorem ; Coaxal circles ; Inversive distance ; Hyperbolic functions --
An introduction to projective geometry : Reciprocation ; The polar circle of a triangle ; Conics ; Focus and directrix ; The projective plane ; Central conics ; Stereographic and gnomonic projection.

A fascinating collection of geometric proofs and propertie